On the Use of Distributed Genetic Algorithms for the Tuning of Fuzzy Rule Based-Systems

  • Ignacio Robles
  • Rafael Alcalá
  • José M. Benítez
  • Francisco Herrera
Part of the Studies in Computational Intelligence book series (SCI, volume 269)


The tuning of Fuzzy Rule-Based Systems is often applied to improve their performance as a post-processing stage once an appropriate set of fuzzy rules has been extracted. This optimization problem can become a hard one when the size of the considered system in terms of the number of variables, rules and, particularly, data samples is big. Distributed Genetic Algorithms are excellent optimization algorithms which exploit the nowadays available parallel hardware (multicore microprocessors and clusters) and could help to alleviate this growth in complexity.

In this work, we present a study on the use of the Distributed Genetic Algorithms for the tuning of Fuzzy Rule-Based Systems. To this end, we analyze the application of a specific Gradual Distributed Real-Coded Genetic Algorithm which employs eight subpopulations in a hypercube topology.

The empirical performance in solution quality and computing time is assessed by comparing its results with those from a highly effective sequential tuning algorithm. We applied both, the highly effective sequential algorithm and the distributed method, for the modeling of four well-known regression problems. The results show that the distributed approach achieves better results in terms of quality and execution time as the complexity of the problem grows.


Genetic Fuzzy Systems Fuzzy Rule Based-Systems Distributed Genetic Algorithms Genetic Tuning 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Driankow, D., Hellendoorn, H., Reinfrank, M.: An introduction to fuzzy control. Springer, Berlin (1993)Google Scholar
  2. 2.
    Pedrycz, W.: Fuzzy Modelling: Paradigms and practice. Kluwer Academic Publishers, Dordrecht (1996)zbMATHGoogle Scholar
  3. 3.
    Palm, R., Driankov, D., Hellendoorn: Model based fuzzy control. Springer, Heidelberg (1997)zbMATHGoogle Scholar
  4. 4.
    Ishibuchi, H., Nakashima, T., Nii, M.: Classification and modeling with linguistic information granules: Advances approaches to linguistic data mining. Springer, Heidelberg (2004)Google Scholar
  5. 5.
    Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst., Man, Cybern. 3, 28–44 (1973)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Goldberg, D.E.: Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, New York (1989)zbMATHGoogle Scholar
  8. 8.
    Holland, J.H.: Adaptation in natural and artificial systems. The University of Michigan Press, Michigan (1975); The MIT Press, London (1992)Google Scholar
  9. 9.
    Cordón, O., Herrera, F., Hoffmann, F., Magdalena, L.: Genetic Fuzzy Systems: evolutionary tuning and learning of fuzzy knowledge bases. World Scientific, Singapore (2001)zbMATHGoogle Scholar
  10. 10.
    Herrera, F.: Genetic fuzzy systems: Taxonomy, current research trends and prospects. Evolutionary Intelligence 1, 27–46 (2008)CrossRefGoogle Scholar
  11. 11.
    Cordón, O., Gomide, F., Herrera, F., Hoffmann, F., Magdalena, L.: Ten years of genetic fuzzy systems: current work and new trends. Fuzzy Sets and Systems 141(1), 5–31 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Eiben, A.E., Smith, J.E.: Introduction to evolutionary computation. Springer, Berlin (2003)Google Scholar
  13. 13.
    Zadeh, L.A.: The concept of a linguistic variable and its applications to approximate reasoning, parts i, ii and iii. Information Science 8, 8, 9, 199–249, 301–357, 43–80 (1975)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Karr, C.: Genetic algorithms for fuzzy controllers. AI Expert 6(2), 26–33 (1991)Google Scholar
  15. 15.
    Herrera, F., Lozano, M., Verdegay, J.L.: Tuning fuzzy logic controllers by genetic algorithms. International Journal of Approximate Reasoning 12, 299–315 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Alcalá, R., Alcalá-Fdez, J., Casillas, J., Cordón, O., Herrera, F.: Hybrid learning models to get the interpretability-accuracy trade-off in fuzzy modeling. Soft Computing 10(9), 717–734 (2006)CrossRefGoogle Scholar
  17. 17.
    Alcalá, R., Alcalá-Fdez, J., Herrera, F.: A proposal for the genetic lateral tuning of linguistic fuzzy systems and its interaction with rule selection. IEEE Transactions on Fuzzy Systems 15(4), 616–635 (2007)CrossRefGoogle Scholar
  18. 18.
    Casillas, J., Cordón, O., del Jesus, M.J., Herrera, F.: Accuracy improvements in linguistic fuzzy modeling. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  19. 19.
    Casillas, J., Cordón, O., del Jesus, M.J., Herrera, F.: Genetic tuning of fuzzy rule deep structures preserving interpretability and its interaction with fuzzy rule set reduction. IEEE Trans. Fuzzy Syst. 13(1), 13–29 (2005)CrossRefGoogle Scholar
  20. 20.
    Cantu-Paz, E.: Efficient and Accurate Parallel Genetic Algorithms. Kluwer Academic Publishers, Norwell (2000)zbMATHGoogle Scholar
  21. 21.
    Fernández de Vega, F., Cantu-Paz, E.: Special issue on distributed bioinspired algorithms. Soft Computing 12(12), 1143–1144 (2008)CrossRefGoogle Scholar
  22. 22.
    Alba, E.: Parallel Metaheuristics: A New Class of Algorithms. Wiley, Chichester (2005)zbMATHGoogle Scholar
  23. 23.
    Sterling, T., Becker, D.J., Savarese, D.F.: How to build a beowulf: A guide to the implementation and application of PC clusters. The MIT Press, Cambridge (1999)Google Scholar
  24. 24.
    Spector, D.H.M.: Building Linux Clusters. O’Reilly, Sebastopol (2000)Google Scholar
  25. 25.
    Dowd, K., Severance, C.: High Performance Computing. O’Reilly, Sebastopol (1998)Google Scholar
  26. 26.
    Robles, I., Alcalá, R., Benítez, J.M., Herrera, F.: Distributed genetic tuning of fuzzy rule-based systems. In: Proceedings of the International Fuzzy Systems Association - European Society for Fuzzy Logic and Technology (IFSA-EUSFLAT) Congress (in press, 2009)Google Scholar
  27. 27.
    Herrera, F., Lozano, M.: Gradual distributed real-coded genetic algorithms. IEEE Transactions on Evolutionary Computation 4(1), 43–63 (2000)CrossRefGoogle Scholar
  28. 28.
    Herrera, F., Martínez, L.: A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans. Fuzzy Syst. 8(6), 746–752 (2000)CrossRefGoogle Scholar
  29. 29.
    Bäck, T., Beielstein, T.: User’s group meeting. In: Proceedings of the EuroPVM 1995: Second European PVM, pp. 277–282 (1995)Google Scholar
  30. 30.
    Punch, W., Goodman, E., Pei, M., Chai-shun, L., Hovland, P., Enbody, R.: Further research on feature selection and classification using genetic algorithms. In: Forrest, S. (ed.) Proceedings of the Fifth International Conference on Genetic Algorithms, pp. 557–564 (1993)Google Scholar
  31. 31.
    Tanase, R.: Distributed genetic algorithms. In: Proceedings of the Third International Conference on Genetic Algorithms, pp. 434–439 (1989)Google Scholar
  32. 32.
    Mülhlenbein, H., Schomisch, M., Born, J.: The parallel genetic algorithm as function optimizer. Parallel Computing 17(6), 619–632 (1991)CrossRefGoogle Scholar
  33. 33.
    Lin, S.C., Punch III, W.F., Goodman, E.D.: Coarse-grain parallel genetic algorithms: Categorization and new approach. In: Proceedings of the Sixth IEEE Parallel and Distributed Processing, pp. 28–37 (1994)Google Scholar
  34. 34.
    Alba, E., Luna, F., Nebro, A., Troya, J.M.: Parallel heterogeneous genetic algorithms for continuous optimization. Parallel Computing 30(5), 699–719 (2004)CrossRefGoogle Scholar
  35. 35.
    Schlierkamp-Voosen, D., Mülhlenbein, H.: Strategy adaptation by competing subpopulations. In: Davidor, Y., Männer, R., Schwefel, H.-P. (eds.) PPSN 1994. LNCS, vol. 866, pp. 199–208. Springer, Heidelberg (1994)Google Scholar
  36. 36.
    Schnecke, V., Vornberger, O.: An adaptative parallel algorithm for vlsi-layout optimization. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 22–27. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  37. 37.
    Alba, E., Dorronsoro, B.: Cellular Genetic Algorithms. Springer, Heidelberg (2008)zbMATHGoogle Scholar
  38. 38.
    Tanase, R.: Parallel genetic algorithm for a hypercube. In: Proceedings of the 2nd International Conference on Genetic Algorithms and their Applications, pp. 177–183 (1987)Google Scholar
  39. 39.
    Cohoon, J.P., Hedge, S., Martin, W.: Punctuated equilibria: A parallel genetic algorithm. In: Proceedings of the 2nd International Conference on Genetic Algorithms and their Applications, pp. 148–154 (1987)Google Scholar
  40. 40.
    Ryan, C.: Niche and species formation in genetic algorithms. In: Chambers, L. (ed.) Practical Handbook of Genetic Algorithms: Applications, pp. 57–74. CRC Press, Boca Raton (1995)Google Scholar
  41. 41.
    Klir, G., Yuan, B.: Fuzzy sets and fuzzy logic; theory and applications. Prentice-Hall, Englewood Cliffs (1995)zbMATHGoogle Scholar
  42. 42.
    Mamdani, E.H.: Application of fuzzy algorithms for control of simple dynamic plant. Proc. Inst. Elect. Eng. 121(12), 1585–1588 (1974)Google Scholar
  43. 43.
    Takagi, T., Sugeno, M.: Fuzzy identification of systems and its application to modelling and control. IEEE Trans. Syst. Man and Cybernetics 15(1), 116–132 (1985)zbMATHGoogle Scholar
  44. 44.
    Alcalá, R., Casillas, J., Cordón, O., Herrera, F.: Building fuzzy graphs: features and taxonomy of learning non-grid-oriented fuzzy rule-based systems. International Journal of Intelligent Fuzzy Systems 11, 99–119 (2001)Google Scholar
  45. 45.
    Au, W.-H., Chan, K., Wong, A.K.C.: A fuzzy approach to partitioning continous attributes for classification. IEEE Transactions on Knowledge and Data Engineering 18(5), 715–719 (2006)CrossRefGoogle Scholar
  46. 46.
    Cordón, O., Herrera, F., Villar, P.: Analysis and guidelines to obtain a good fuzzy partition granularity for fuzzy rule-based systems using simulated annealing. International Journal of Approximate Reasoning 25(3), 187–215 (2000)zbMATHCrossRefGoogle Scholar
  47. 47.
    Yager, R., Filev, D.: Essentials of fuzzy modeling and control. John Wiley and Sons, Chichester (1994)Google Scholar
  48. 48.
    Kuncheva, L.: Fuzzy classifier design. Springer, Heidelberg (2000)zbMATHGoogle Scholar
  49. 49.
    Casillas, J., Cordón, O., Herrera, F., Magdalena, L.: Interpretability issues in fuzzy modeling. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  50. 50.
    Gürocak, H.B.: A genetic-algorithm-based method for tuning fuzzy logic controllers. Fuzzy Sets and Systems 108(1), 39–47 (1999)zbMATHCrossRefGoogle Scholar
  51. 51.
    Mamdani, E.H., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man-Machine Studies 7, 1–13 (1975)zbMATHCrossRefGoogle Scholar
  52. 52.
    Eshelman, L.J.: The CHC adaptive search algorithm: How to have safe serach when engaging in nontraditional genetic recombination. In: Rawlin, G.J.E. (ed.) Foundations of genetic Algorithms, vol. 1, pp. 265–283. Morgan Kaufman, San Francisco (1991)Google Scholar
  53. 53.
    Eshelman, L.J., Schaffer, J.D.: Real-coded genetic algorithms and interval-schemata. Foundations of Genetic Algorithms 2, 187–202 (1993)Google Scholar
  54. 54.
    Kröger, B., Schwenderling, P., Vornberger, O.: Parallel genetic packing on transputers. In: Parallel Genetic Algorithms: Theory and Applications: Theory Applications, pp. 151–186 (1993)Google Scholar
  55. 55.
    Baker, J.E.: Adaptive selection methods for genetic algorithms. In: Proceedings of the First International Conference on Genetic Algorithms and their Applications, pp. 101–111. Erlbraum Associates, Hillsdale (1985)Google Scholar
  56. 56.
    Baker, J.E.: Reducing bias and inefficiency in the selection algorithm. In: Proceedings of the 2nd International Conference on Genetic Algorithms, ICGA 1987 (1987)Google Scholar
  57. 57.
    Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer, Heidelberg (1992)zbMATHGoogle Scholar
  58. 58.
    Alcalá-Fdez, J., Sánchez, L., García, S., del Jesus, M.J., Ventura, S., Garrell, J.M., Otero, J., Romero, C., Bacardit, J., Rivas, V.M., Fernández, J.C., Herrera, F.: KEEL: A software tool to assess evolutionary algorithms to data mining problems. Soft Computing 13(3), 307–318 (2009)CrossRefGoogle Scholar
  59. 59.
    Wang, L.X., Mendel, J.M.: Generating fuzzy rules by learning from examples. IEEE Trans. Syst. Man and Cybernetics 22(6) (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Ignacio Robles
    • 1
  • Rafael Alcalá
    • 1
  • José M. Benítez
    • 1
  • Francisco Herrera
    • 1
  1. 1.Dept. of Computer Sciences and Artificial IntelligenceUniversity of GranadaGranadaSpain

Personalised recommendations